Does the union of two events mean exactly one of the events occurs, or can both happen?

Conditions

• E and F are events in a probability space.

Reasoning, step by step

1. Identify the union symbol $\cup$.
2. Translate the symbol to the English word 'or'.
3. Apply the mathematical definition of 'or' in set theory, which is inclusive.
4. Conclude that the union includes outcomes where E happens, F happens, or both happen.

Example

The speaker explicitly states, 'remember this union is like or in the English language, so E or F, potentially both.'

Common misconceptions

• Treating the union as an exclusive 'or', which would incorrectly exclude the case where both events happen.
• Confusing the union $\cup$ with the intersection $\cap$.

Watch the explanation

Explore next

• What is the inclusion-exclusion formula for two events E and F?
• Why do we subtract the intersection when computing the probability of the union of two events?
• When should the inclusion-exclusion principle be used?